Speed of Light a constant?
AA
the Milky way, and possibly within. Could someone enlighten my thoughts
on this issue.
It has been shown that light will change course due to gravatational
wells around a star, and a slight change in direction will occur thus
leading the postulation that the photon has some very small mass. If
one considers intergalactic travel of light, wouldn't light also be
effected in the third dimention; speed. I would think that light would
not only change direction, but also velocity as it enters and exits the
galactic garvitational wells that exist.
Thank You,
Kevin Longbrake
Student
Phillip Helbig---remove CLOTHES to reply
writes:
The LOCALLY MEASURED speed of light is constant. The rest-mass of the
photon is 0, despite the gravitational bending of light. There IS a
delay effect, though, called the Shapiro delay. It has been measured.
It is generally thought of not as a slowing of the speed of light, but
rather as a stretching of space.
Uncle Al
Photon velocity (vector) changes, photon speed (scalar) does not. All
inertial observers observe an identical lightspeed. Lorentz
invariance demands it.
http://arXiv.org/abs/gr-qc/9909014
Amer. J. Phys. 71 770 (2003)
Phys. Rev. Lett. 92 121101 (2004)
falling light
Physics Today 57(7) 40 (2004)
http://physicstoday.org/vol-57/iss-7/p40.shtml
No aether
http://fsweb.berry.edu/academic/mans/clane/
http://physicsweb.org/articles/world/17/3/7
No Lorentz violation
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz3.pdf
harry
"Phillip Helbig---remove CLOTHES to reply" <hel...@astro.multiCLOTHESvax.de>
wrote in message news:efrk3i$fii$1...@online.de...
Indeed, as Helbig stressed, the essential point is that the speed of light
is c in any LOCAL measurement system. Not all textbooks make this
sufficiently clear. Another essential point is that using a Newtonian
reasoning of "falling particles" you would get a speeding-up effect, while
in reality there is a "Shapiro DELAY" effect.
For non-local considerations it can be handy as well as enlightening to use
one single inertial reference system far away from stars in free space and
in which the star is approximately at rest. When you use such a reference
system the speed of light near the sun as well as on earth is reduced and is
a function of gravitational potential. See also:
http://www.physlink.com/Education/AskExperts/ae13.cfm
You can see Einstein's 1916 Huygens light bending approach in:
http://www.alberteinstein.info/gallery/gtext3.html (near the end, p.198).
Cheers,
Harald
mark...@yahoo.com
> Photon velocity (vector) changes, photon speed (scalar) does not. All
> inertial observers observe an identical lightspeed. Lorentz
> invariance demands it.
Well, there's the catch-22. What constitutes a locally inertial frame
is determined by the metric; i.e. a frame locally inertial at point x
is one whose coordinate charge has {mn,r} = 0 at x.
A fluctuation in the metric also entails a fluctuation in the field of
locally inertial frames. Thus, if L is inertial at x under the metric
g, then under the metric g + dg, L is slightly accelerating at x.
Consequently, the determination of light speed, itself, acquires an
effective fluctuation dependent on dg; and an uncertainty dependent on
whatever uncertainty may exist in g.
There is a different conclusion that also arises out of this
consideration. In quantum field theory, one learns that the field
vacuum for an inertial frame isn't even seen as a pure quantum state,
at all, in an accelerating frame, but as a thermal state. A thermal
mixture is an *incoherent*, *classical* mixture of states, not a
quantum superposition and resides in an entirely different sector from
the pure states associated with the accelerating frame's 'vacuum".
Though these objects are global, one might envision there to be a local
approximation of them such that a *local* frame that is inertial at a
given point x will yield something like an approximate vacuum which,
when seen from the point of view of a frame that is non-inertial at x
will appear as a thermal state that resides in an inequivalent sector
of state space.
The fluctuation in the metric g -> g + dg pushes the inertial frames in
too accelerating frames. Consequently, the vacuua of g are seen as
slightly thermalized, slightly classically-mixed, states when the
metric is at g + dg.
Because of this, the states which reside in the background metric g can
*not* coherently superpose with those that reside in the background
metric g + dg. The corresponding result in quantum theory would be that
the two coherent states |g> and |g + dg> that represent these metrics
would, themselves, reside in different sectors.
The fluctuation g -> g + dg therefore can NOT be seen as a quantum
fluctuation at all and cannot participate in coherent superpositions!
The field, itself, is essentially classical.
These are also conclusions that had been arrived at by independent
means by Sardanashvily, who is fairly well-known for his "gauge
gravitation" programme; and who copublished "Gauge Gravitation Theory"
along with Zakharov in 1992.
The conclusion they drew was in reference to the breaking of the world
symmetry from a local GL(4) group to the local Lorentz group that the
presence of fermions engenders. The quotient GL(4)/Lorentz plays an
analogous role that it would in the symmetry breaking of the Higgs
phenomena. Each sector comprises a separate vacuum phase (and separate
sector in state space). Fluctuations of the associated "Goldstone"
fields are essentially classical and can only be regarded as quantum
fluctuations in a "quasi-particle" approximation.
The fields which embody the GL(4) -> Lorentz symmetry breaking are none
other than the tetrad fields h, out of which the metric g is
constructed.
It also dovetails consistently with the argument posed by Jacobson
(1995, his paper that derives GR from the laws of thermodynamics as a
consequence of the Bekenstein bound), who points out that gravitation
should no more be quantized as a fundamental field to yield gravitons,
than the "sound" field in a solid should. Instead, the gravitons are to
be regarded as analogous to phonons, rather than fundamental quantum
particles in their own right.
Igor Khavkine
> "Phillip Helbig---remove CLOTHES to reply" <hel...@astro.multiCLOTHESvax.de>
> wrote in message news:efrk3i$fii$1...@online.de...
> > The LOCALLY MEASURED speed of light is constant. The rest-mass of the
> > photon is 0, despite the gravitational bending of light. There IS a
> > delay effect, though, called the Shapiro delay. It has been measured.
> > It is generally thought of not as a slowing of the speed of light, but
> > rather as a stretching of space.
>
> Indeed, as Helbig stressed, the essential point is that the speed of light
> is c in any LOCAL measurement system. Not all textbooks make this
> sufficiently clear. Another essential point is that using a Newtonian
> reasoning of "falling particles" you would get a speeding-up effect, while
> in reality there is a "Shapiro DELAY" effect.
>
> For non-local considerations it can be handy as well as enlightening to use
> one single inertial reference system far away from stars in free space and
> in which the star is approximately at rest. When you use such a reference
> system the speed of light near the sun as well as on earth is reduced and is
> a function of gravitational potential. See also:
> http://www.physlink.com/Education/AskExperts/ae13.cfm
Let me clear up some misconseptions that may be deduced from the above
statement. First, once gravity (and hence space-time curvature) is
involved there cannot be a single *intertial* coordinate system that
encompases both a region far away from any massive stars and the stars
themselves. Then best one can do is settle for a *locally inertial*
coordinate system that can force the metric to appear Minkoswki-like
only at a single point. In a small neighborhood of that point, if
space-time curvature is small enough to be neglected, the same
coordinate system can be considered approximately inertial. The size of
this "small" neighborhood is obviously bigger far away from any massive
object than when close to one, where curvature becomes important.
Second, the speed of light is not a geometric invariant, and thus it's
problematic to talk of comparing its value at different space-time
points, at least without specifying precisely how it's defined or
measured. There is one sense in which the "speed of light" can be said
to vary in in space as well as direction. Take any coordinate system
(t,x,y,z), where t is a time-like coordinate, while the others are
space-like coordinates. Then let c be the slope of the light cone, as
computed in the chosen coordinate system, at any point covered by the
coordinate system, in any direction emanating from it. Quite obviously,
the quantity c will depend on all of the following: coordinate system,
space-time point, direction. If one defines the "speed of light" to be
the quantity c, then it can be meaningfully said to not be constant in
space, time, and even direction. However, the non-existence of a
preferred family of space-time coordinate systems on curved space-times
(such as the family of global inertial frames in Minkowski space), one
cannot meaningfully talk about what the value of c is and how it
actually changes without specifying a coordinate system. But then,
there are so many to choose from, and one's preference may not be
another's.
> You can see Einstein's 1916 Huygens light bending approach in:
> http://www.alberteinstein.info/gallery/gtext3.html (near the end,
> p.198).
The above definition of c is what Einstein uses in this reference. At
the time, differential geometry was not as developed as it is today. So
Einstein was forced to use an arbitrarily chosen coordinate system,
even though all physical results had to be proven to be independent of
any such choice. Today, such arbitary choices no longer need to be
made, and physical results are approached from a much more geometric
standpoint. Early papers on GR, while possibly enlightening in other
respects, are not a great reference on the (often subtle) distinction
between coordinate-dependent and purely geometric effects.
There is another way to define the speed of light: through operational
measurements. Under this definition, it always yields the same value.
An operational definition of speed requires an existing definition of a
unit of time and a unit of distance. The SI second[1] is as good a unit
as any. It uses the duration of on cycle of radiation emitted as a
particular spectral line of the Cesium 133 atom. Unfortunately, for the
purposes of this setup, the SI definition of the meter[2] is not good,
because it is defined as a function of the speed of light. But any
other length standard can be used. For instance, even the SI meter was
defined for a while in terms of the wavelength of a certain spectral
line of krypton 86. Lets use this older standard as the definition of
the meter in our setup.
So, take any region of space the size of an atomic physics laboratory,
and assume that within it space-time curvature can be neglected. Place
a light source at point A, and equip this point with an atomic clock
set to count seconds in the way we've defined them above. Then place a
mirror at point B, which is interferometrically measured to be one
meter away from point point A. This distance is calibrated according to
the above chosen definition of the meter. The experiment consists of
sending out a pulse of light from point A to point B, with only vacuum
in between, and awaiting its return. The time interval between the
emission of return of the pulse at point A is recorded. The atomic
clock reports this interval to be 2/299792458 seconds. The same
number, 2/299792458, is again reported when the roles of points A and B
are swapped. The same number is reported if another similar laboratory
is constructed in a completely different region of space-time.
So, in the sense of the above operational definition, the speed of
light is constant, everywhere and everywhen. Personally, I prefer this
definition to the above. Other's tastes may differ, but that's only the
more reason to be specific about what you favorite definition of the
"speed of light" is.
[1] http://www.bipm.fr/en/si/si_brochure/chapter2/2-1/second.html
[2] http://www.bipm.fr/en/si/si_brochure/chapter2/2-1/metre.html
Hope this helps.
Igor